Many studies have reported correlations between the activity of sensory neurons and animals' judgments in discrimination tasks (Choice Probability, or CP). Although this demonstrates a link between the activity of individual sensory neurons and perception, it also raises new questions. In particular, it is not understood why neurons in some areas show decision-related activity whereas equally selective and informative neurons in other areas do not. For discrimination tasks, decision-related activity often depends on the tuning preferences of the neuron and increases with a neurons sensitivity for the task. This suggests that the correlation reflects a specific link between task-relevant sensory neurons and the animals perceptual choice. Nonetheless, the interpretation of such decision-related activity has proven difficult. In particular, it is complicated by the presence of inter-neuronal correlations (noise-correlations) typically observed between pairs of sensory neurons. Recent theoretical work demonstrated an important law that holds regardless of these correlations. If a population of neurons is read out with an optimal linear decoder, there is a fixed relationship between CP and the sensitivity of a given neuron to the relevant sensory variable. An especially strong test of this is to examine CP and sensitivity in a set of neurons for two different tasks. We performed these measurements in neurons recorded from area V2 of macaque monkeys trained to report perceived depth, based on binocular disparity. In one version of the task (fine) very small disparity magnitudes, with no stimulus noise, were used. In the second version (coarse), large disparities were used, but the signal was degraded by adding noise in the stimulus. While the data for coarse disparity discrimination were compatible with predictions for an optimal linear read-out corrupted by information-limiting correlations, our results for the fine disparity discrimination task were not. This suggests that the brain may apply different decoding rules to the neurons in visual cortex, even for very similar tasks.